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On the upper part load vortex rope in Francis turbine: Experimental investigation

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2010 IOP Conf. Ser.: Earth Environ. Sci. 12 012053

(http://iopscience.iop.org/1755-1315/12/1/012053)

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with pulsation sras it is illustrated in Fig. 2. Haban et al.[6] demonstrated that the elliptical shape of the vortex ropecan be predicted by modal analysis of a simplified draft tube flow. Koutnik et al.[7] analyzed the influence of airinjection and hydraulic circuit on the upper part load pressure fluctuations. The elliptical shape of the vortex rope wasalso investigated using PIV measurements by Kirschner et al.[8] on a simplified draft tube.

This paper is a contribution to the analysis of the upper part load pressure fluctuations by means of high speedcamera visualization with synchronized measurement of pressure fluctuations. First, the test case and relatedexperimental apparatus is described. Then, image post processing is used to derive vortex rope diameter time

evolution and to compare with to synchronized pressure fluctuations. The influence of both sigma cavitation numberand Froude number are analyzed to show the interaction between the upper part load fluctuations and the hydrauliccircuit.

Fig. 1Waterfall diagram of the pressure fluctuations measured at the downstream cone of the draft tube

Fig. 2Elliptical vortex rope precessing in the draft tube cone at upper part load

2.Case study and experimental apparatus

Pressure fluctuations measurements with synchronized draft tube vortex rope visualizations are carried out on ascale model Francis turbine with specific speed =0.5 installed in EPFL test rig, see Fig. 3. The waterfall diagram ofthe pressure fluctuations in the draft tube cone are presented in Fig. 1. The operating point featuring upper part loadpressure fluctuation at rated discharge of 83% of the best efficiency point is selected for the experimental

investigation and the related operating conditions are summarized in table 1.To perform the visualization of the vortex rope, a high speed camera Photron is used. The frame rate used for the

investigation is 4000 frames/seconds using a diaphragm aperture time of 1/4000 s and a number of 3600 frames permovie. The images are obtained with a resolution of 1024512 pixels. The lighting is ensured by 2 continuous spotlights of 600 W each located at 45of each side of the high speed camera as shown in Fig. 3. The Francis turbinescale model is equipped with 3 wall Quartz pressure transducers Kistler 701A measuring the unsteady part of the

pressure. Two pressure transducers are located in the draft tube cone and the third one is located in the spiral case

inlet, see Fig. 3. The synchronization between the pressure acquisition and the image records is ensured by the triggerof an oscilloscope. The oscilloscope is used to store one second time history pressure signal with a sampling rate of

sr

2

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12.5 kHz. In parallel, the pressure is recorded using an HP 3566A PC Spectrum/Network Analyser system butwithout synchronization with the camera. These measurements are used for the representation of the waterfalldiagram of the pressure fluctuations obtained by the averaging of 8 pressure amplitude spectra based on 4 secondspressure time history with a sampling rate of 256 Hz.

Table 1 Parameter of the scale model Francis turbine and investigated operating point

Specific speed of the machine

[-]BEP/

[-]BEP/

[-]

N[rpm]

GVO[]

0.50 0.832 1.00 700 21.5

Fig. 3Scale model installed on the EPFL test rig with high speed camera visualization

3.Influence of the cavitation number

The influence of the cavitation number , is analyzed for the operating point of

Table 1 by considering 6 different cavitation numbers varying from = 0.1 to 0.3 and keeping the Froudenumber constant. The operating parameters as well as the observations are reported in the Table 2.

Table 2 Operating parameters for the influence of the cavitation number

N [-] Froude Number [-] N[rpm]

Observation

1 0.30 8.47 700 Hydroacoustic resonance,strong vortex rope shock on draft tube wall

2 0.26 8.47 700 Random hydroacoustic resonance,vortex rope shock on draft tube wall

3 0.22 8.47 700

4 0.18 8.47 700

5 0.14 8.47 700 Low inter-blade cavitation development

6 0.10 8.47 700 Strong inter-blade cavitation development

The pressure fluctuations measured at the upstream cone, downstream cone and spiral case for the 6 differentoperating points are presented in Fig. 4 as a waterfall diagrams. It can be noticed that the frequency of the pressurefluctuations in the range of 1 to 3 times the rotational speed increases with the cavitation number, similar to [4]. Thefrequencies and amplitudes related to the upper part load pressure fluctuations are reported in Fig. 5. The frequency

increases almost linearly with the cavitation number while the amplitude of the pressure pulsations rises quickly up to2.5% of the specific energy E for = 0.3. The amplitudes of pressure fluctuations for this cavitation number are

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similar for the 3 pressure transducers. In addition, strong mechanical vibrations and noise were noticed during themeasurements. The shock phenomenon was also strongly present for these operating conditions. Thus, this operatingpoint corresponds to the resonance between the vortex rope and the test rig.

Figure 6 left presents pictures of the vortex rope extracted from the movie synchronized with the pressuremeasurements presented on the top of the figure. This figure depicts the elliptical shape of the vortex rope selfrotating at the pulsation srand precessing with a pulsation ropefor the resonance operating conditions, i.e.= 0.3.The five successive pictures extracted from the movie correspond to one period of the pressure fluctuations of

interest T*; from t = toto t = to+ T*. Moreover, the influence of the pressure on the dimensions of the vortex ropeappears clearly, as for t = to, when the pressure is high, the vortex rope features small diameter while the diameter is

the highest for t = to + T*/2 when the pressure is the lower. This pressure dependency is identical for the 6 operatingpoints, see Nicolet [9]. Figure 6 right presents the same results for cavitation number = 0.22 where it can be noticedthat, as expected, the mean diameter of the vortex rope increases as the cavitation number decreases. Moreover, thepressure fluctuations feature smaller amplitudes and a random like pattern. By analyzing the pictures of Fig. 6 it isfound in agreement with Koutnik et al. [5], that the pulsation of the self rotation of the elliptical vortex rope sris halfthe pulsation of the measured pressure fluctuations *. Therefore, the combination between the rope precession rope

and the pressure fluctuations associated with the self rotation of the rope

*, leads to the modulation process alreadydescribed by Arpe [10]. The elliptical shape of the vortex rope makes apparent the non-uniformity of the pressure

distribution in the cross section of the cone. Consequently, if the elliptical vortex rope rotates with the pulsation sr,the associated pressure fluctuation features a pulsation of *= 2 sr.

Fig. 4 Waterfall diagram of the pressure fluctuations measured at the downstream cone (left), upstream cone(center) and the spiral case (right) as function of the frequency and cavitation number

Fig. 5 Evolution of the frequency and amplitude of the pressure pulsations as function of the cavitationnumber at the downstream cone

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Fig. 6 Evolution of the vortex rope development for operating point N1(left) and operating point N2 (right),see Table 2

4.Vortex rope volume time evolution

To confirm the influence of the pressure fluctuations on the vortex rope volume, the images of the movie relatedto operating point N1 with = 0.3 are post processed. The post processing methodology is described in Fig. 7. First,a part of the image focusing on the vortex rope is extracted. Then, the image is filtered in order to obtain black and

white image of the vortex rope. The black area of the image Aband the white area of the image Aware computed interms of pixels enabling to compute the ratio of white area as Aw/(Aw+Ab). This ratio is representative of the vortexrope diameter. This image processing is carried out for all the 3600 images of the movie of operating point N1 with= 0.3 and are presented as function of time in Fig. 8 left. The pressure fluctuation time history is presented in thisfigure and synchronized in time with the time evolution of the vortex rope volume using the camera start trig. It canbe noticed that, as identified from Fig. 6, the volume of the vortex rope is always maximum when the pressure isminimum and vice versa. The period of the pressure fluctuations T* and the period of the vortex rope precession Tropecan be clearly identified. Moreover, the ratio of white area calculated from image processing is represented as afunction of the pressure in the draft tube and in spiral case for one period of pressure fluctuation T* in Fig. 8 right. It

can be noticed that the curves related to the pressure in the cone feature breathing like pattern and describe surfacescounter-clockwise indicating that the vortex rope is providing energy to the hydraulic system and behaves as an

energy source.

Fig. 7 Image post processing for vortex rope volume time history determination

Image

Extraction Image Post Processing

Aw Ab

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Fig. 8 Time evolution of the vortex rope area and synchronized pressure fluctuations (left)and vortex rope area versuspressure (right)

5.Influence of the Froude number

The operating conditions chosen for the investigation of the influence of the Froude number are identical as the

previous operating point in terms of discharge coefficient and specific energy coefficient given in

Table 1, but the cavitation number is kept constant and equal to = 0.30 in order to focus on the conditions of

resonance of the test rig. The Froude number is given byrefref LgCFr = which can be expressed, considering

the reference velocity as ECref = as follows:

refLHFr = (1)

The Froude number affects the distribution of cavitation in the flow as it determines the pressure gradient

relatively to the size of the machine. The relation between the position of the vapor pressure pvcan be expressed as a

function of the Froude number, see Franc et al. [11], neglecting Reynolds effects, assuming the same cavitationnumber as a function of the reference position Zrefas follows:

2

2

2

1

2

1

Fr

Fr

ZZ

ZZ

ref

ref=

(2)

The Froude number being usually smaller on prototype than in the model, the elevation of the position of thecavitation is higher on prototype than in the model, [11], and [12]. Due to the difference of Froude numbers, the

vortex rope on scale model is more narrow and longer than on prototype as illustrated in Fig. 9, see Drfler [13].For these investigations, four different values of the Froude number are taken into account and are obtained by

varying the rotational speed of the turbine. The operating conditions considered for this investigation are presented inthe Table 3. The wall pressure fluctuations measured at the downstream cone, upstream cone and spiral case arepresented as function of the frequency and Froude number in Fig. 10 as waterfall diagram.

Fig. 9 Difference of the cavitation development between model (M) and prototype (P) due to difference inFroude numbers

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.2 0.4 0.6 0.8 1.0

Time [s]

Pressure[bar],

Aw/(Aw+Ab)[-]

Downstream Cone

Upstream cone

trigger

Spiral case

Aw/(Aw+Ab)

T*

Trop

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Table 3 Operating conditions for the influence of the Froude number

N [-] Froude Number [-] N [rpm] Remark

1 0.30 8.47 700 Hydroacoustic resonance,and mechanical vibrations

7 0.30 7.86 650 Hydroacoustic resonance,

and mechanical vibrations

8 0.30 7.26 600 Low hydroacoustic resonance,and mechanical vibrations

9 0.30 6.64 550 Low hydroacoustic resonance,

and mechanical vibrations

First, it can be noticed from the observations of Table 3 that hydroacoustic resonance and mechanical vibrationsare observed for all tested conditions, even if the level of resonance and related vibration were lower for lower valuesof the Froude number. This is due to the fact that increasing the Froude number leads to a reduction of the specificenergy and therefore of the absolute magnitude of the pressure fluctuations. However, as it is reported by the

waterfall diagram of Fig. 10, the relative amplitudes of pressure fluctuations are not affected in the same way. Figure11 represents the amplitude and frequency of the pressure pulsations of interest as function of the Froude number. It

can be noticed that the frequency of the pressure pulsations are proportional to the runner rotational speed, inaccordance with Koutnik et al.[7], and that the amplitudes are of the same order of magnitude for the values ofFroude equal to Fr = 8.47 and 7.86, while they are divided at least by a factor 2 for Fr = 7.26 and 6.64. The reason isthat the resonance phenomenon features more random behavior for Fr = 7.26 and 6.64 than for Fr = 8.47 and 7.86,see Nicolet [9]. Consequently the values obtained in the waterfall diagram are smaller for the higher values of Froudenumber.

No visualizations of the vortex rope are presented here as the shape of the vortex rope was not very muchaffected by the Froude number, at least in the range of tested Froude values, and therefore does not affect

significantly the wave speed in the draft tube. It means that the eigen frequencies of the test rig, including the turbineand the draft tube, are not strongly affected by the change of the Froude number in the tested range. Then changingthe rotational speed of the runner results in a mistuning between the excitation source, illustrated by the vortex rope

self rotation, with associated pressure pulsation *, and the eigen frequency of the test rig. It results in a situationwhere there is no more strict resonance but random resonance. This means that the observed phenomenon is really ofthe resonance type. Similar conclusions have been found by Koutnik et al. [5] who found also a small part of self

excitation observing the pressure versus rope volume dependence.The modulation process between the vortex rope precession and the pressure associated with self rotation of the

vortex rope, fropeandf* respectively, is illustrated by the amplitude spectra measured for Fr = 7.86. Therefore, the

time plots and related amplitude spectra are represented in Fig. 12 where it can be clearly seen that modulationbetween the two dominant pulsations leads to amplitudes in the spectrum forf = f*frope, f* 2 frope, f* 3 frope,etcand forf = 2 f* frope, f*2 frope, f*3 frope, etc. It can be noticed that in this case, the self rotation of the vortex ropecorresponds to a multiple of the vortex rope precession frequency.

Fig. 10 Waterfall diagram of the pressure fluctuations at the downstream cone (left), upstream cone (center) andthe spiral case (right)as function of the frequency and Froude number for = 0.3

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Fig. 11 Evolution of the frequency and amplitude of the pressure pulsations as function of the Froude number

at the downstream cone for = 0

Fig. 12 Modulation of the pressure pulsation at the vortex rope precession frequencyfropeand pressure pulsationf*for = 0.3 and Froude =7.86

6.Conclusion

An experimental investigation on a reduced scale Francis turbine of specific speed = 0.5 was performed

using wall pressure measurements synchronized with movie recording. The upper part load is characterized bypressure pulsations in the range of f/n = 1 to 3. The flow visualizations with simultaneous pressure

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measurements show that the vortex rope features an elliptical cross section and that the vortex rope is selfrotating at a frequency half of pressure fluctuations of interest. This particular structure of the flow leads tomodulation of the pressure fluctuations related to the vortex rope precession and of the pressure fluctuations ofinterest.

Image processing enabled to point out that the vortex volume is changing according to pressure and featuresbreathing like pattern and behaves as an excitation source. The pressure fluctuations appear to be strongly linkedto the cavitation number and therefore resonance conditions are commonly encountered during model tests when

the excitation source of the vortex rope in the range of f/n = 1 to 3 matches the hydraulic system eigenfrequencies. The Froude investigation shows that the pressure fluctuation frequency is proportional to therotational speed, and therefore the draft tube flow behaves as an excitation source but with excitation frequenciesabove the rotational speed.

Acknowledgments

The authors would like to thank Etienne Vuadens, Amborsio Acal Ganaza and Philippe Ausoni from LMHfor their help in the setup of the acquisition system and signal post processing. The authors also would like to

thank all the staff from the model testing group of the Laboratory for Hydraulic Machines, LMH, for theirsupport for the set up of the experimental facilities.

Nomenclature

A

C

E

Fr

H

refL N

Q

refR

TZf

ropef *f

n

Image area, pixels

Absolute mean flow speed, m/s, C Q A=

Machine specific energy,J/kg, 1 2E gH gH=

Froude number,

Head, m

Reference length, m

Rotational speed, rpm

Flow rate, m3/s, Q C A= Machine reference radius, m

Period, s

Elevation, m

Frequency, Hz, Tf 1= Frequency of the vortex rope precession, Hz

Frequency of the vortex rope self rotation

pressure fluctuations, Hz

Runner rotational frequency, Hz

vp

rope *

BEP

Pressure, Pa.

Vapor pressure, Pa

Gravity acceleration, m/s2

Water density, kg/m3

Discharge coefficient,3refQ R =

Specific energy coefficient,2 22 refE R =

Machine specific speed,1/ 2 3 / 4

= Pulsation, rad/s

Pulsation of the vortex rope precession,

rad/s

Pulsation of vortex rope self rotation

pressure fluctuations, rad/s

Cavitation number,

( ) 22/1 refvref Cpp = Best efficiency point

References

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[13]

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